**Common Names:** Unsharp Filter, Unsharp Sharpening Mask

The unsharp filter is a simple sharpening operator which derives its name from the fact that it enhances edges (and other high frequency components in an image) via a procedure which subtracts an unsharp, or smoothed, version of an image from the original image. The unsharp filtering technique is commonly used in the photographic and printing industries for crispening edges.

Unsharp masking produces an edge image from an input image via

where is a smoothed version of . (See Figure 1.)

Figure 1Spatial sharpening.

We can better understand the operation of the unsharp sharpening filter by examining its frequency response characteristics. If we have a signal as shown in Figure 2(a), subtracting away the lowpass component of that signal (as in Figure 2(b)), yields the highpass, or `edge', representation shown in Figure 2(c).

Figure 2Calculating an edge image for unsharp filtering.

This edge image can be used for sharpening if we add it back into the original signal, as shown in Figure 3.

Figure 3Sharpening the original signal using the edge image.

Thus, the complete unsharp sharpening operator is shown in Figure 4.

Figure 4The complete unsharp filtering operator.

We can now combine all of this into the equation:

where *k* is a scaling constant. Reasonable values for *k* vary
between 0.2 and 0.7, with the larger values providing increasing
amounts of sharpening.

The unsharp filter is implemented as a window-based operator, *i.e.* it
relies on a
convolution
kernel to perform spatial
filtering. It can be implemented using an appropriately defined
lowpass filter to produce the smoothed version of an
image, which is then pixel subtracted from the original
image in order to produce a description of image edges, *i.e.* a
highpassed image.

For example, consider the simple image object

whose strong edges have been slightly blurred by camera focus. In order to extract a sharpened view of the edges, we smooth this image using a mean filter (kernel size 3×3) and then subtract the smoothed result from the original image. The resulting image is

(Note, the gradient image contains positive and negative values and, therefore, must be normalized for display purposes.)

Because we subtracted all low frequency components from the
original image (*i.e.*, we highpass filtered the image)
we are left with only high frequency edge descriptions. Normally, we
would require that a sharpening operator give us back our original
image with the high frequency components enhanced. In order to achieve
this effect, we now add some proportion of this gradient
image back onto our original image. The image

has
been sharpened according to this formula, where the
scaling constant *k* is set to 0.7.

A more common way of implementing the unsharp mask is by using the negative Laplacian operator to extract the highpass information directly. See Figure 5.

Figure 5Spatial sharpening, an alternative definition.

Some unsharp masks for producing an edge image of this type are shown
in Figure 6. These are simply negative, discrete Laplacian
filters. After convolving an original image with a kernel such as one of
these, it need only be scaled and and then
added to the original. (Note that in the
Laplacian of Gaussian worksheet, we demonstrated edge
enhancement using the correct, or *positive*, Laplacian and LoG
kernels. In that case, because the kernel peak was positive, the edge
image was subtracted, rather than added,
back into the original.)

Figure 6Three discrete approximations to the Laplacian filter.

With this in mind, we can compare the unsharp and Laplacian
of Gaussian filters. First, notice that the gradient images produced
by both filters (*e.g.*

produced by unsharp and

produced by LoG) exhibit the side-effect of
*ringing*, or the introduction of additional intensity image
structure. (Note also that the rings have opposite signs due to the
difference in signs of the kernels used in each case.) This ringing
occurs at high contrast edges. Figure 7 describes how
oscillating (*i.e.* positive, negative, positive, *etc.*) terms in the
output (*i.e.* ringing) are induced by the oscillating terms in the
filter.

Figure 7Ringing effect introduced by the unsharp mask in the presence of a 2 pixel wide, high intensity stripe. (Gray levels: --1=Dark, 0=Gray, 1=Bright.)a)1-D input intensity image slice.b)Corresponding 1-D slice through unsharp filter.c)1-D output intensity image slice.

Another interesting comparison of the two filters can be made by examining their edge enhancement capabilities. Here we begin with reference to

The image

shows the sharpened version produced by a 7×7 Laplacian of Gaussian. The image

is that due to unsharp sharpening
with an equivalently sized Laplacian. In comparing the
unsharp mask defined using the Laplacian with the LoG, it is obvious
that the latter is more robust to noise, as it has been designed
explicitly to remove noise before enhancing edges. Note, we can
obtain a slightly less noisy, but also less sharp, image using a
smaller (*i.e.* 3×3) Laplacian kernel, as shown in

The unsharp filter is a powerful sharpening operator, but does indeed produce a poor result in the presence of noise. For example, consider

which has been deliberately corrupted by Gaussian noise. (For reference,

is a mean filtered version of this image.) Now compare this with the output of the unsharp filter

and with the original image

The unsharp mask has accentuated the noise.

*Adaptive Unsharp Masking*

A powerful technique for sharpening images in the presence of low noise levels is via an adaptive filtering algorithm. Here we look at a method of re-defining a highpass filter (such as the one shown in Figure 8) as the sum of a collection of edge directional kernels.

Figure 8Sharpening filter.

This filter can be re-written as times the sum of the eight edge sensitive kernels shown in Figure 9.

Figure 9Sharpening filter re-defined as eight edge directional kernels

Adaptive filtering using these kernels can be performed by filtering the image with each kernel, in turn, and then summing those outputs that exceed a threshold. As a final step, this result is added to the original image. (See Figure 10.)

Figure 10Adaptive sharpening.

This use of a threshold makes the filter adaptive in the sense that it overcomes the directionality of any single kernel by combining the results of filtering with a selection of kernels --- each of which is tuned to an edge direction inherent in the image.

You can interactively experiment with this operator by clicking here.

- Consider the image
which, after unsharp sharpening (using a mean smoothing filter, with kernel size 3×3) becomes

**a)**Perform unsharp sharpening on the raw image using a Gaussian filter (with the same kernel size). How do the sharpened images produced by the two different smoothing functions compare?**b)**Try re-sharpening this image using a filter with larger kernel sizes (*e.g.*5×5, 7×7 and 9×9). How does increasing the kernel size affect the result?**c)**What would you expect to see if the kernel size were allowed to approach the image size? - Sharpen the image
Notice the effects on features of different scale.

- What result would you expect from an unsharp sharpening operator
defined using a smoothing filter (
*e.g.*the median) which does not produce a lowpass image. - Enhance the edges of the 0.1% salt and pepper noise
corrupted image
using both the unsharp and Laplacian of Gaussian filters. Which performs best under these conditions?

- Investigate the response of the unsharp masking filter to edges
of various orientations. Some useful example images include
and

Compare your results with those produced by adaptive unsharp sharpening.

**R. Haralick and L. Shapiro** *Computer and Robot Vision*,
Addison-Wesley Publishing Company, 1992.

**B. Horn** *Robot Vision*, MIT Press, 1986, Chap. 6.

**A. Jain** *Fundamentals of Digital Image Processing*,
Prentice-Hall, 1989, Chap. 7.

**R. Schalkoff** *Digital Image Processing and Computer
Vision*, John Wiley & Sons, 1989, Chap. 4.

Specific information about this operator may be found here.

More general advice about the local HIPR installation is available in the
*Local Information* introductory section.